Exploratory Galois Theory

ISBN-13: 9780521544993 / Angielski / Miękka / 2004 / 222 str.

John Swallow

Opis

Combining a concrete perspective with an exploration-based approach, this analysis develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and only requires knowledge of a first course in abstract algebra. It introduces tools for hands-on experimentation with finite extensions of the rational numbers for readers with Maple or Mathematica. Please visit the author's website at: http: //www.davidson.edu/academic/math/swallow/john.htm

Recenzje

'The exploration-based approach to the subject is very down-to-earth, entertaining, motivating, encouraging and enlightening, making the text highly suitable for undergraduate courses, for seminars, or for self-paced independent study by interested beginners.' Zentralblatt MATH

Spis treści

1. Preliminaries; 2. Algebraic numbers, field extensions, and minimal polynomials; 3. Working with algebraic numbers, field extensions, and minimal polynomials; 4. Multiply-generated fields; 5. The Galois correspondence; 6. Some classical topics; Historical note.